1. Agent-based Simulation of Financial Markets Ilker Ersoy

2. Introduction  Simulation of financial markets is a new fast growing research area.  Main motivations are  to provide a testbed for automation of financial markets  To provide thought experiments to understand the “moods” of markets which can’t be explained by Rational Expectations theory.

3. Markets as Complex Systems  Financial markets are complex systems with behaviors such as bubbles and crashes.  This complexity defies traditional mathematical analysis.  The complexity arises from the interactions and expectations of the agents (buyers,sellers,etc.) in the market.  Agent-based market simulation is one of the applications of Artificial Life.

4. Rational Expectations Theory  Conventional RE theory assumes that  Agents deduce their optimum behavior by logical processes.  Agents have full knowledge of the market.  Agents know that others work with same knowledge on the same rational basis.  These assumptions are too strong, in most cases simply not true for financial markets.  RE theory does not explain dynamic behavior of markets.

5. Agent-based Simulation  In a real financial market, there are heterogeneous agents with different expectations and different levels of knowledge.  Agent-based simulation takes this approach to create an artificial market.  Agents start with little rationality and specialized knowledge and adapt or learn becoming experts in their domains.

6. Agent-based Simulation  Advantages:  None of the assumptions of RE theory is required.  Even the modeler does not need to have the knowledge to derive an optimum solution for each agent.  This approach is not deductive, this is much closer to normal human behavior.  This approach is inductive not deductive, this is much closer to normal human behavior.

7.  Advantages:  This approach is applicable in situations where RE theory produces no answers due to lack of single well-defined equilibrium solution.  This approach can predict and interpret dynamical behaviors, not only the final outcome.

8.  Disadvantages:  Lack of analytic methods, it is largely computational.  Multitude of possible algorithms for learning and adaptation.  Sensitivity to parameters such as learning rate.

9. Implementation  Agents use learning classifier systems (LCS) to gather knowledge and assess their rules.  Each rule is assessed by the outcome of the execution of that rule (gain or loss).  Rules are eliminated by genetic approach, new rules are created by mutation and crossover.

10. Implementation  LCS classifies the environment (market) into classes.  Each bit represents the existence of a certain condition in the market or for a stock.  Agents place their bids for stocks, and price is established according to supply and demand.

11. Experiments  A number of experiments can be conducted in this setting.  Different agents can be created representing different investor classes for a realistic market simulation.  Experiments show that even this simple simulation is able to produce complex dynamic behavior such as bubbles and crashes.

12. Problems and Future Directions  Establishing stock prices need a realistic clearing mechanism, not studied broadly by far.  LCS is suitable for genetic approach but might not be suitable to represent realistic knowledge about market.  Calibration to real markets should consider the fact that investors have a long history of knowledge of the market to learn from.